This article has been helpful in understanding the new access specifiers in Swift 3. It also gives some examples of different usages of fileprivate
In Swift 4.0, Private is now accessible in extension but within same file. If you declare/define extension in other file, then your private variable will not be accessible to your extension**
File Private
File-private access restricts the use of an entity to its own defining source file. Use file-private access to hide the implementation details of a specific piece of functionality when those details are used within an entire file.
Syntax: fileprivate
Example: fileprivate class SomeFilePrivateClass {}
Private
Private access restricts the use of an entity to the enclosing declaration, and to extensions of that declaration that are in the same file. Use private access to hide the implementation details of a specific piece of functionality when those details are used only within a single declaration.
Syntax: private
Example: private class SomePrivateClass {}
Here is more detail about all access levels: Swift - Access Levels
Look at this images:
File: ViewController.swift
Here extension and view controller both are in same file, hence private variable testPrivateAccessLevel is accessible in extension

File: TestFile.swift
Here extension and view controller both are in different files, hence private variable testPrivateAccessLevel is not accessible in extension.


Here class ViewController2 is a subclass of ViewController and both are in same file. Here private variable testPrivateAccessLevel is not accessible in Subclass but fileprivate is accessible in subclass.
